Transformation techniques for decision diagrams in computer-aided design

Bibliography 95 Introduction In 1943, Thomas Watson, founder of IBM, remarked that he thought that there was a \ w orld market for maybe ve computers." In 1949, the American magazine \Popular mechanics" reported optimistically that computers in the future might weigh no more than 1.5 tons. In 1977, Ken Olsen, founder of Digital Equipment, scooed that \there is no reason anyone wants a computer at home." In 1997, there were tens of millions of computers, either at a place of work or at home. An advanced workstation may have a Gigabyte of main memory, its processor consists of several million transistors and can do a billion operations per second. These historical facts and anecdotes may illustrate the rapid developments in the area of VLSI (Very Large Scale Integration) digital circuits and computer technology. Moreover, it may not be surprising that the design of circuits and systems with several million parts is a very diicult task and has raised problems which are far beyond the scope of manual design. Over the last three decades, Computer-Aided Design (CAD) tools have therefore been adopted for various tasks of the design process. Nowadays, these tools have not only become widely used, but they are indispensable. However, applications in information processing, telecommunication or in industrial control systems permanently require the construction of even more powerful high-speed circuits. On the one hand, this imposes bigger and bigger challenges upon the CAD systems. On the other hand, all these systems underlie the inherent complexity in the manipulation of switching functions which has been extensively studied in theoretical computer science Weg87, Mei89]. One of the main problems is to 1 2 Introduction get the immense number of combinations of mathematical objects, the so-called combinatorial explosion, under control. A central problem in the design of CAD systems for VLSI circuits is the representation of the functional behavior of a circuit. For an illustration we will shortly consider the problem of combinational circuit veriication. Hereby it is to check whether a combinational circuit C satisses a given speciication S. F or the solution of this problem computer-internal representations for C and S have to be determined which can then be used to test the relevant properties. Of course, this approach only leads to a practical procedure, if bothrepresentations can becomputed eeciently and practical algorithms are available to decide equivalence, satissability and similar properties by means of the representations. The …